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U-M ME 555 - Plant/Control Optimization of a PEM

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Dongsuk Kum & Scott MouraME 555 – Design Optimization, Winter 2007 Slide 1 of 16Plant/Control Optimization of a PEM Plant/Control Optimization of a PEM Hybrid Fuel Cell Vehicle to Grid (V2G) Hybrid Fuel Cell Vehicle to Grid (V2G) SystemSystemDongsukDongsukKumKumScott MouraScott MouraME 555 ME 555 --Winter 2007Winter 2007Professor Professor PanosPanosY. Y. PapalambrosPapalambrosApril 16, 2007April 16, 2007Dongsuk Kum & Scott MouraME 555 – Design Optimization, Winter 2007 Slide 2 of 16Outline• Introduction• Modeling– Fuel Cell System & Battery– Supervisory Controller– System Level Block Diagram & Power Cycle• Optimization Problem Summary• Model Analysis– DOE study– Monotonicity Analysis– Surrogate Model• Optimization Study– Optimal Solution and Constraint Activity– Lagrange Multipliers and Constraint Relaxation• Parametric Study• Discussion of ResultsDongsuk Kum & Scott MouraME 555 – Design Optimization, Winter 2007 Slide 3 of 16Introduction• Fuel Cell technology– Abundant energy source H2– High efficiency (50-70%)– Clean energy source (zero emissions)• Hybrid Technology– Hybrid concept is developing in many engineering fields, esp. the auto industry– Fuel Cell/Battery leverages advantages of each energy source• V2G Concept– Enables the use of renewable energy sources– Adds energy storage capacity element to grid– Distributed generation (DG) decentralizes grid– 5% of California’s vehicle fleet can provide 10% peak power for entire state [1]– Consumer may sell power back to the grid– More expensive FCV becomes a more profitable investment[1] W. Kempton, J. Tomic, S. Letendre, A. N. Brooks and T. Lipman, "Vehicle-to-grid power: Battery, hybrid, and fuel cell vehicles as resources for distributed electric power in California," California Air Resources Board, Tech. Rep. UCD-ITS-RR-01-03, June 2001, 2001.Dongsuk Kum & Scott MouraME 555 – Design Optimization, Winter 2007 Slide 4 of 16Fuel Cell System & BatterymaxmaxmaxQdtIQSOCQICOSbattbatt∫−=⇒−=intint224RRPVVIbattococbatt−−−=),,(intRVsocfPocbatt=),(,),(intTsocfRTsocfVoc==Isothermal Operation AssumptionBATTERYCOMPRESSORH2 STORAGE TANKSUPPLY MANIFOLDCOOLER & HUMIDIFIERCOMPRESSOR MOTORAir SupplyH2FUEL CELL STACKVoltageCATHODE SIDEANODE SIDEPOWER BUSStackCurrentStackVoltageBattery PowerPower OutputResistive Equivalent Circuit Model• List of components–FC stack– Humidifier– Supply Manifold– Compressor• Main functions of battery modelFuel Cell stack model from Jay PukrushpanBattery model from ADVISORDongsuk Kum & Scott MouraME 555 – Design Optimization, Winter 2007 Slide 5 of 16Rule-based Controller0 0.5 1 1.5 2 2.5 3x 10400.10.20.30.40.50.60.70.80.91 Fuel Cell System Efficiency vs. PowerFC System Power (W)EfficiencyPower Assist modeFuel Cell only modeBatteryonly modePpa_modePbatt_modepa_modedembattpa_modefcPPPPP−==,chargebattchargedemfcPPPPP−=+=,dembattfcPPP==,0()deschargechargeSOCSOCKP−=where• The idea of the rule-based control is to operate the fuel cell within a desired operating region that achieves high efficiency.• For low power demand, battery provides all necessary power and fuel cell is turned off.• For high power demand, battery assists fuel cell providing power to grid, which allows FC operate in higher efficiency region.Dongsuk Kum & Scott MouraME 555 – Design Optimization, Winter 2007 Slide 6 of 16System Level Block Diagram & Power CycleFuel Cell SystemPower DemandRule-based Supervisory ControllerFuel Cell SystemBatteryBattery Power DemandGrid PowerDemand CycleElectricPowerBusHydrogen Fuel• Representative grid power demand cycle• Adapted from CAISO daily demand forecast• Scaled for medium size office or apartment complex• Augmented with white Gaussian noise to simulate stochastic nature of power demand6am 9am 12am 3am 6pm 9pm 12pm 3pm 6am67891011 Grid Power Demand CycleTime (hour)Power Demand (kW)Grid Power Demand CycleDongsuk Kum & Scott MouraME 555 – Design Optimization, Winter 2007 Slide 7 of 16Optimization Problem SummaryMinimize hydrogen fuel consumption with respect to6 Design Variables– Number of fuel cells in stack, nfc– Number of battery modules, nbatt– Compressor size, λcp– Power Assist (PA) mode threshold, Ppa– Battery mode threshold, Pbatt– Controller Gain, Kchsubject to10 Constraints– Fuel cell stack length– Battery weight– Stack heat generation– Parasitic losses– Fuel cell efficiency– Oxygen excess ratio– Max/Min SOC– Start/End SOC deviation()()chbattpaBATTFCCPHKPPnnmf ,,,,,min2λ=xDongsuk Kum & Scott MouraME 555 – Design Optimization, Winter 2007 Slide 8 of 16DOE StudyPurpose: Determine general trends and possible monotonic relationships• Sensitivity– Most sensitive to variations of power threshold values– Least sensitive to number of cells & battery modules• Critical Role of Control– Optimal control allows the use of less efficient component sizes• Monotonicity– Power threshold variables– Number of cells & battery modules (if fluctuations are ignored)• Optimal Solution– Fluctuations indicate possible local minima30035040045050010203040500.0750.080.0850.090.0950.10.105Number of CellsNumber of Battery ModulesH2 Consumption (kg)(a)800090001000011000640066006800700072000.0650.070.0750.080.0850.09Batt ModeThreshold (W)PA ModeThreshold (W)H2 Consumption (kg)(b)1001011020.511.520.080.090.10.110.12Charge GainCompressor ScaleH2 Consumption (kg)(c)Dongsuk Kum & Scott MouraME 555 – Design Optimization, Winter 2007 Slide 9 of 16Monotonicity Analysis• Active Constraints– Fuel Cell Stack Length ACTIVE MP1 wrt nfc– Battery Weight ACTIVE by MP1 wrt nbatt–Minimum SOC ACTIVE by MP1 wrt {nfcλcp PpaPbattKch}• Solutionsnfc*= 421nbatt*= 3410010110210203040500.40.50.60.7Charge GainBattery ModulesMin SOC(b)80009000100001100065700075000.40.50.60.7Batt Mode (W)PA Mode (W)Min SOC(a)Dongsuk Kum & Scott MouraME 555 – Design Optimization, Winter 2007 Slide 10 of 16Surrogate Model• Motivation– Noisy objective function– Gradient-based optimization is best suited for continuous, smooth objective functions• Artificial Neural Network (ANN)– Two-layer feed-forward neural network (FFNN)– Generalized regression neural network (GRNN)– Trained via Levenberg-Marquardt algorithm, a quasi-Newton optimization technique• Input/Output Model– 6 inputs (design variables)– 1 output (objective function)–56= 15625 total training sets300 320 340 360 380


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